CC-486 and Nivolumab for the Treatment of Hodgkin Lymphoma Refractory to PD-1 Therapy or Relapsed

Inclusion Criteria: * Documented informed consent of the participant and/or legally authorized representative * Assent, when appropriate, will be obtained per institutional guidelines * Be willing to provide tissue from a fresh core or excisional biopsy (performed as standard of care) of a tumor lesion prior to starting study therapy or from archival tissue of a biopsy that was performed after the most recent systemic therapy * Exception may be granted by the principal investigator (PI) if a biopsy is not feasible and/or safe * Age: \>= 18 years * Eastern Cooperative Oncology Group (ECOG) =\< 2 * Histologically confirmed diagnosis of classical Hodgkin lymphoma (excluding nodular lymphocyte predominant Hodgkin lymphoma) according to the World Health Organization (WHO) classification, with hematopathology review at the participating institution * Refractory to PD-1/PD-L1 directed immunotherapy, defined as patients who had prior exposure to PD-1/PD-L1 immunotherapy and either: * Achieved a best response of PD, or * Achieved a best response of CR/PR but developed PD while on active PD-1/PD-L1 treatment or within 12 weeks of last dose of PD-1/PD-L1 treatment * Relapse must have been confirmed histologically (with hematopathology review at the participating institution) * Exceptions may be granted with study PI approval * Patient must have received at least one prior systemic therapy and must not currently be candidate for stem cell transplantation * Measurable disease by computed tomography (CT) or positron emission tomography (PET)/CT scan with one or more sites of disease \>= 1.5 cm in longest dimension * Fully recovered from the acute toxic effects (except alopecia) to =\< Grade 1 to prior anti-cancer therapy * Absolute neutrophil count (ANC) \>= 1,000/mm\^3 * NOTE: Growth factor is not permitted within 7 days of ANC assessment unless cytopenia is secondary to disease involvement * Platelets \>= 75,000/mm\^3 * NOTE: Platelet transfusions are not permitted within 7 days of platelet assessment unless cytopenia is secondary to disease involvement * Hemoglobin \>= 8 g/dL * Total bilirubin =\< 1.5 x upper limit of normal (ULN) or =\< 3 x ULN if patient has Gilbert's disease OR direct bilirubin =\< ULN for subjects with total bilirubin levels \> 1.5 x ULN * Aspartate aminotransferase (AST) =\< 2.5 x ULN OR =\< 5 x ULN for subjects with liver involvement by lymphoma as the etiology of transaminase elevation * Alanine aminotransferase (ALT) =\< 2.5 x ULN OR =\< 5 x ULN for subjects with liver involvement by lymphoma as the etiology of transaminase elevation * Creatinine clearance of \>= 40 mL/min per 24 hour urine test or the Cockcroft-Gault formula * If not receiving anticoagulants: International normalized ratio (INR) OR prothrombin (PT) =\< 1.5 x ULN * If on anticoagulant therapy: PT must be within therapeutic range of intended use of anticoagulants * If not receiving anticoagulants: Activated partial thromboplastin time (aPTT) =\< 1.5 x ULN * If on anticoagulant therapy: aPTT must be within therapeutic range of intended use of anticoagulants * Women of childbearing potential (WOCBP): negative urine or serum pregnancy test * If the urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required * Agreement by females and males of childbearing potential\* to use an effective method of birth control or abstain from heterosexual activity for the course of the study through at least 5 months after the last dose of nivolumab and 6 months after the last dose of CC-486 for females, and 3 months after the last dose of CC-486 for males with female partners of reproductive potential * Childbearing potential defined as not being surgically sterilized (men and women) or have not been free from menses for \> 1 year (women only) Exclusion Criteria: * Prior allogeneic stem cell transplant within 6 months prior to day 1 of protocol therapy * If prior allogeneic transplant, then no active graft-versus-host disease (GVHD), no systemic immunosuppression for at least 3 months prior to study enrollment, and no history of grade 3-4 acute GVHD * Autologous stem cell transplant within 3 months prior to day 1 of protocol therapy * Prior solid organ transplant * Systemic steroid therapy for lymphoma symptom control must be tapered down to =\< 10 mg/day prednisone or equivalent * Live vaccine within 30 days prior to day 1 of protocol therapy * Concomitant investigational therapy * History of prior \>= grade 3 hypersensitivity to nivolumab, or history of allergic reactions attributed to compounds of similar chemical or biologic composition to study agents or to any of the excipients, including mannitol * Known active central nervous system (CNS) involvement by lymphoma * History of active pneumonitis or interstitial lung disease requiring supplemental oxygen or corticosteroid treatment * History of inflammatory bowel disease (e.g., Crohn's disease, ulcerative colitis), celiac disease (i.e., sprue), prior gastrectomy or upper bowel removal, or any other gastrointestinal disorder or defect that would interfere with the absorption, distribution, metabolism or excretion of the study drug and/or predispose the subject to an increased risk of gastrointestinal toxicity * History of another primary malignancy that has not been in remission for at least 2 years, with the following exceptions: * Adequately treated non-melanoma skin cancer or lentigo maligna (melanoma in situ) without evidence of disease * Adequately treated in situ carcinomas (e.g. cervical, esophageal) without evidence of disease * Asymptomatic prostate cancer managed with a watch-and-wait strategy * If the malignancy is expected to not require any treatment for at least 2 years (this exception should be discussed with the study PI) * History of progressive multifocal leukoencephalopathy (PML) * Prior diagnosis of inherited or acquired immunodeficiency * Active, known or suspected autoimmune disease. The following are exceptions: * Vitiligo * Psoriasis not requiring systemic treatment * Hemolytic anemia associated with the lymphoma * Type I diabetes mellitus, if adequately controlled with therapy * Thyroid disease, if adequately controlled with therapy * Any autoimmune disease should have not been treated with systemic disease-modifying antirheumatic drugs for the last 2 years. All patients with a history of autoimmune disease except for the above should be discussed with the study PI * Uncontrolled systemic fungal, bacterial or viral infection (defined as ongoing signs/symptoms related the infection without improvement despite appropriate antibiotics, antiviral therapy and/or other treatment) * Clinically significant uncontrolled illness * History of a cerebral vascular event (stroke or transient ischemic attack), unstable angina, myocardial infarction, or cardiac symptoms consistent with New York Heart Association Class III-IV within 6 months prior to day 1 of protocol therapy * Known active hepatitis B virus (HBV) or hepatitis C virus (HCV) infection. Patients with past HBV infection (defined as negative hepatitis B surface antigen \[HBsAg\] and positive hepatitis B core antibody \[HBcAb\]) are eligible if HBV deoxyribonucleic acid (DNA) is undetectable. Patients who are positive for HCV antibody are eligible if polymerase chain reaction (PCR) is negative for HCV ribonucleic acid (RNA). Testing to be done only in patients suspected of having infections or exposures * Known active human immunodeficiency virus (HIV) infection. Subjects who have an undetectable or unquantifiable HIV viral load with CD4 \> 200 and are on highly active antiretroviral therapy (HAART) medication are allowed. Testing to be done only in patients suspected of having infections or exposures * Females only: Pregnant or breastfeeding * Prospective participants who, in the opinion of the investigator, may not be able to comply with all study procedures (including compliance issues related to feasibility/logistics)